Question 601853
(tan30 + tan45)
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(1 - tan30 tan45) 

= (1/sqrt3 + 1)
----------------- 
(1 - (1/sqrt3)(1)) 

= [(1 + sqrt3) / sqrt3]
-------------------- 
  [(sqrt(3)-1)]/sqrt(3)]

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Invert the denominator and multiply:
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= [(1 + sqrt3) / sqrt3]*[sqrt(3)/(1 -sqrt(3))]
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Cancel the common sqrt(3) to get:
= [1+sqrt(3)]/[(1-sqrt(3))]
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Multiply numerator and denominator by (1+sqrt(3) to get
----
= [1+sqrt(3)]^2 / [1-3]
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= [1 + 2sqrt(3) + 3]/(-2)
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= [4 + 2sqrt(3)]/(-2)
----
= -2 -sqrt(3)
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Cheers,
Stan H.